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Overview
Table of Contents
IB Goals
The IB Syllabus for Z-Scores requires IB Students to know following things:
- Standardization of normal variables (z- values).
- Probabilities and values of the variable must be
found using technology. - The standardized value (z) gives the number of
standard deviations from the mean
- Probabilities and values of the variable must be
- Inverse normal calculations where mean and
standard deviation are unknown- Use of z-values to calculate unknown means and
standard deviations.
- Use of z-values to calculate unknown means and
Z-Score
Introduction to the Z-Score
The Z-Score (also called Z-Value or Standard Score) describes how far away from the mean a certain data point is. It’s a measure of how many standard deviations a raw score is from the population mean.
That means that the standard deviation is the unit of measurement of the z-value. It allows for comparisons between different normal distributions.
When the Z-Score is positive, then the value lies above the mean. When it is negative, then it lies below the mean.
Z-Scores range from -3 to +3.
In order to calculate the Z-Score one must know the mean and standard deviation of the normal distribution.
Z-Value Formula
The Z-Score is calculated by finding the difference between the raw score and the population mean and dividing that by the population standard deviation.
Need more Practice with basic Z-Scores? Check out these practice questions.
Why do we need Z-Scores?
Z-Scores are useful because they let us compare scores from different distributions.
How do we interpret Z-Scores?
Since a Z-Score tells you how many standard deviations a raw score is from the mean we have collected some common scenarios for a Z-Score.
- If Z<0, then the raw score is below the mean
- If Z>0, then the raw score is above the mean
- If Z=o, then the raw score is the mean
- If Z=1, then the raw score is one standard deviation above the mean. If Z=2, then the raw score is two standard deviations from the mean, etc.
- If Z=-1, then the raw score is one standard deviation below the mean. If Z=-2, then the raw score is two standard deviations below the mean.
- In a normal distribution 68% of raw scores have a Z-Score between 1 and -1. 95% of raw scores have a Z-Score between 2 and -2. And 99% have a Z-Score between -3 and 3.
Finding the Z-Values with a Calculator
Z-Score Table
You can find the Z-Score Table here.
Z-Score Calculator
You can find the Z-Score Calculator here.
Inverse Normal Distribution
Introduction to the Inverse Normal Distribution
The Inverse Normal Distribution is not a distribution. It is an informal term that describes a method of find the x-value from a known probability.
Extra Resources
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